Honestly, I don't think Joel put much thought into the whole Firefly/vaccine thing because for a long time, he didn't want any part in it. He reluctantly takes on the job due to insistence from Tess, and only continues it for a time out of obligation to her, and even tries to dump the responsibility of transporting Ellie onto his brother. Even when he finally decides to help Ellie of his own volition, he still asks her if she wants to turn around, instead of completing the journey.
I think that it's clear that he really didn't care one way or another about the vaccine (and thus didn't seem to give it much though), not to mention that it is a bit of an assumption to expect Joel to deduce that Ellie had to die to study the immunity without more information.







